In this PhD thesis we analyse splitting methods for two wave type equations.
We investigate the Lie and the Strang splitting for the cubic nonlinear Schrödinger equation on the full space and on the torus in up to three spatial dimensions. We prove that the Strang splitting converges in $L^2$ with order $1+\theta$ for initial functions in $H^{2+2\theta}$ with $\theta\in (0,1)$ and that both splitting schemes converge with order one for initial functions in $H^2$. We confirm the theoretical convergence orders by numerical experiments.
Furthermore, we analyse an altern... mehrating direction implicit time splitting scheme for the Maxwell equations with sources, currents and conductivity. We show that it is efficient, that it converges with order two in $L^2$ and in a weak sense, and that it preserves the divergence conditions up to order one in $L^2$ and in a weak sense. We confirm the $L^2$-results by numerical experiments.